Physics 21 Fall, 2004 Solution to HW-26 34 P62 A 130 × astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens? We must Fnd the focal lengths of the objective ( f o = x ) and the eyepiece ( f e = y ). Their ratio is the power, and their sum is the length (since the eye is relaxed, the image of the objective is just at the focal length of the eyepiece, so the eye is focused on the image at inFnity. We work in cm: x y = 130 ⇒ x = 130 y x + y = 125 ⇒ x = 125 − y Equating the two expressions for x , we Fnd 130 y = 125 − y ⇒ 131 y = 125 ⇒ y =0 . 954 Substituting back, we have f e =0 . 954 cm ,f o = 124 cm 35 P8 Suppose a thin piece of glass were placed in front of the lower slit so that the two waves enter the slits 180 ◦ out of phase. Describe in detail the interference pattern on the screen. The pattern will have the dark spot at the center, because the waves with equal path lengths will interfere destructively. The spacing of successive fringes will be the same as if the waves were in phase.
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